Answer:
(x - 3)² - 11--------------------------
GivenExpression x² - 6x - 2.Convert this to vertex form by completing the square.
Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:
x² - 6x - 2 = x² - 2*3*x + 3² - 3² - 2 = (x - 3)² - 9 - 2 = (x - 3)² - 11Answer:
[tex](x-3)^2-11[/tex]
Step-by-step explanation:
Given quadratic expression:
[tex]x^2-6x-2[/tex]
To write the given expression in the form (x + a)² + b, complete the square.
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies x^2-6x+\left(\dfrac{-6}{2}\right)^2-2-\left(\dfrac{-6}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2-6x+\left(-3\right)^2-2-\left(-3\right)^2[/tex]
[tex]\implies x^2-6x+9-2-9[/tex]
The first three terms x² - 6x + 9 form a perfect square trinomial.
A perfect square trinomial can be written as the square of a binomial.
Factor the perfect square trinomial:
[tex]\implies(x-3)^2-2-9[/tex]
Simplify:
[tex]\implies(x-3)^2-11[/tex]
Therefore, the given expression written in the form (x + a)² + b is:
[tex]\boxed{(x-3)^2-11}[/tex]
rhonda's cell phone plan cost 50$ per month plus 0.25 for each text she sends, how many text messages can she send and still pay less than a total of 70$
The text messages that Rhonda can send and still pay less than a total of $70 is less than 80 messages.
How many text messages can she send?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the number of tests be represented by t.
The inequality will then be:
50 + 0.25t < 70
0.25t < 70 - 50
0.25t < 20
Divide
t < 20/0.25
t < 80
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Solve the compound inequality and graph on the number lines provided.
7) -2 x ≤ 4 AND 10>-2 x
8) 10<3 x-2 or -3 x-2>14
The compound inequality solved are:
x ≤ 2 and x > -5
x > 4 or x < -5.3
The graph of the number line is given above.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
-2 x ≤ 4 and 10 > -2x
x ≤ 4/-2 and 10/2 > -x
x ≤ -2 and 5 > -x
x ≤ 2 and x > -5
This means.
-5 < x ≤ 2
The number line can be graphed as,
<----__-5__-4__-3__-2__-1__0__1__2__3__4__5----->
o---------------------------------------- o
10 < 3x - 2 or -3x - 2 > 14
10 + 2 < 3x or -3x > 14 + 2
12 < 3x or -3x > 16
x > 4 or -x > 16/3
x > 4 or x < -16/3
x > 4 or x < -5.3
x > 4 can be represented on a line graph as,
__-1__0__1__2__3__4__5__6__7--------->
o----------------------->
x < -5.3 can be represented on a number graph as,
<---------8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4---------->
<--------------------------o
Thus,
The compound inequality solved are:
x ≤ 2 and x > -5
x > 4 or x < -5.3
The graph of the number line is given above.
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Which could be the first step in solving the equation represented by the model below?
Add 4 positwe unt tles to each side.
Remove 4 unit ties from each side.
Add 6 positive unit tiles to each side.
Remove 6 unit tiles from each side.
To each side, add 4 positive unit tiles.
What is a one-variable linear equation and what does it look like?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.
The initial formula is:
3x - 4 = 2x + 5
Four positive unit tiles are added to each side, giving us:
3x - 4 + 4 = 2x + 5 + 4
3x = 2x + 9
which removes the independent elements off both sides of the equal sign and places them all on the right side (the +9 term), simplifying the initial equation. You'll see that the other choices don't produce this outcome.
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find the 16th term of the arithmetic sequence whose common difference is d=7 and whose first term is a↓1=-2
The 16th term of the arithmetic sequence value is 103.
How to find 16th term of the arithmetic sequence?The 16th term of the arithmetic sequence whose common difference is d=7 and whose first term is a↓1=-2
An arithmetic sequence is defined as an=a1+d (n-1). In essence, this indicates that the term you're looking for, an, is equal to the first term, a1, plus the term difference, d, times the number of terms, n, minus one. For this issue, that essentially means that
an=a1+d(n-1)
The value of an at term sixteen is equal to -2 + 7*. (16-1)
PEDMAS is used to
a16= -2+7*15
a16= -2+105
a16= 103
Therefore, 103 will be the 16th term's value.
The 16th term of the arithmetic sequence value is 103.
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Evaluate the absolute of w if w = -8 -5
Answer:
13
Step-by-step explanation:
w = -8 -5 =-13=13
On Kate's reading app, she eams one star for every six books she reads. So far she has read 1.590 booksHow many stars has she earned?
Answer:
265
Step-by-step explanation:
1590/6=265
265x1=265
Simplify please!
Sqrt(-256x^8)
please help me mickey and how do I do brainlest your so smart
Answer:
second option or B
And to mark brainliest on answers when 2 people answer a crown button will appear on the bottom right and you click that
Step-by-step explanation:
-7+4x>-3
+7. +7
4x>4
/4. /4
x>1
So second option is correct
Hopes this helps sorry for late response I was eating
Simplify the expression using properties of operations 7 1/3t-(10 2/3t-6)
The result is 6-13/3×t after simplification by multiplying first and added the like term.
What do you mean by properties of operation?The procedure of calculation which we use in arithmetic. We perform our mathematical calculation by using particular operational properties such as addition, subtraction, multiplication and division.
How do we simplify mathematical terms?we can simplify any expression by using the properties of addition, subtraction, multiplication or division depending on the statement given.
in the above expression 7×(1/3)t- [10×(2/3)t-6]
we simplify it (7/3)t- (20/3)t+6
-(13/3)t+6
hence, 6-13/3t
hence, the result is 6-13/3×t
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A school club visits. a museum, Students tickets cost $ 6. Non- student ticket’s cost $12. The club paid $240 for tickets. (1) Define variables (1) Create an equation that models this situation (2) Rewrite equations slope intercept form.
"Define variables"
→ The number of student's tickets = a
→ The number of non-student tickets = b
→ the total cost represented = y
"Create an equation that models this situation"
→ y = $5 × a + $10 × b
"Rewrite the equation in slope intercept form"
→ y = $5 × a + $10 × b
→ y = 5a + 10b
→ 250 = 5a + 10b
Write an equation in slope intercept form
Answer:
y = 2x - 5
Step-by-step explanation:
slope = 1-(-3)/3-1
4/2 = 2
this is the m value, or value before x.
So far, this is what we have: y = 2x + b
To find b, we plug in one of the points we have, into the equation.
(in this case ill use (3, 1), where 3 is the x and 1 is the y)
So,
1 = 2(3) + b
1 = 6 + b
1 - 6 = b
-5 = b
Finally,
y = 2x - 5
You take a vacation with your family to Cancun, Mexico. One day you decide to rent a jet ski while at the beach. The equation T=
0.55m 5 gives the total cost in dollars T for renting a jet ski for m minutes. What is the cost for renting a jet ski for 35
minutes?
Answer:
19.25
Step-by-step explanation:
t = .55m
t = .55(35)
t = 19.25
I am not sure what you mean by 5 give the total cost in dollars T. I am not sure where the comes from.
Answer:
$24.25
Step-by-step explanation:
Given equation:
[tex]T=0.55m+5[/tex]
where:
T = total cost of renting a jet ski (in dollars)m = number of minutesTo find the total cost of renting a jet ski for 35 minutes, substitute m = 35 into the given equation and solve for T:
[tex]\implies T=0.55(35)+5[/tex]
[tex]\implies T=19.25+5[/tex]
[tex]\implies T=24.25[/tex]
Therefore, the total cost of renting a jet ski for 35 minutes is $24.25.
Suppose you have just obtained a 30-year home mortgage for $120,000 at an APR of 5%. Find the required monthly payment.
The required monthly payment is given as follows:
$644.22.
What is the monthly payment formula?The monthly payment is defined by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The parameters are listed as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the values of these parameters are given as follows:
P = 120000, r = 0.05, n = 30 x 12 = 360.
Then:
r/12 = 0.05/12 = 0.004167.
Hence the monthly payment is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 120000\frac{0.004167(1.004167)^{360}}{(1.004167)^{360} - 1}[/tex]
A = $644.22.
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How many unit cubes would you need to create a tower that was 7 units tall and 3 units deep?
Jenny has five exam scores of 100 , 83 , 96 , 84 , and 98 in her biology class. What score does she need on the final exam to have a mean grade of 90 90 ? Round your answer to two decimal places, if necessary. (All exams have a maximum of 100 100 points.)
Jenny needs to score 79 on final exam.
How to add decimal places?A decimal separator is a symbol that separates the integer and fractional parts of a decimal number. Different countries have officially designated various symbols to be used as separators. The symbol chosen also influences the symbol used for the thousands separator in digit grouping. Rounding to two decimal places is the same as rounding to the hundredths place, which is the second place to the right of the decimal point. 2.83620364, for example, can be rounded to two decimal places as 2.84, and 0.7035, to two decimal places as 0.70.
Total marks divide by total number subjects=Average
100+88+96+84+98+x=90*6
461+x=540
x=79
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evaluate: x2 - y2 by replacing x with 1/2 and y with 1/4
[tex]x^2 - y^2[/tex] when x = 1/2 and y = 1/4
[tex]\frac{1}{2} ^2 - \frac{1}{4} ^2\\\\=\frac{1}{4}-\frac{1}{16} \\\\= \frac{4}{16}-\frac{1}{16}\\ \\= 3/16[/tex]
Find an equation for the parabola that has its vertex at the origin and satisfies the given condition. Directrix y=1/2
Required equation of the parabola with origin as its vertex and directrix
y = 1/2 is equal to x² = -2y.
As given in the question,
Let vertex of the parabola be ( h, k )
Vertex of the given parabola be at origin
⇒ ( h , k ) = ( 0 , 0 )
Directrix is y =1/2 above the vertex.
Focus is ( 0, -1/2)
Equation of the parabola is given by
Distance between focus to the vertex = distance between vertex to the directrix
( y - (1/2) )² = ( x - 0)² + ( y - (-1/2) )²
⇒ y² - y + 1/4 = x² + y² + y + 1/4
⇒ -y = x² + y
⇒x² = -y - y
⇒ x² = -2y
Therefore, the equation of the parabola with vertex at origin and directrix y =1/2 is equal to x² = -2y .
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The sequence negative one fifth comma two sixths comma negative three sevenths comma four eighths and so on is given.
Part A: Assuming the pattern continues, list the next four terms in the sequence. Show all necessary math work. (4 points)
Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points)
Part C: Is the sign of f (56) positive or negative? Justify your reasoning mathematically without determining the value of f (56). (2 points)
PLEASE ANSWER IN THE FORMAT AS
A;
B;
C;
The answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.
What is a sequence?
A sequence is defined as an arrangement of numbers in a particular order.
A sequence is given ; -1/5, 2/6, -3/7, 4/8.....
Part A
From inspection of the sequence, the pattern is:
i) Add 1 to the numerator of the previous term.
ii) Add 1 to the denominator of the previous term.
iii) Make every other term negative.
Therefore, The next four terms are -5/9, 6/10, -7/11, 8/12
Part B
From inspection of the sequence, we can see that the numerator is the position of the term (n) in the sequence. So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.
The denominator is 5 more than the position of the term in the sequence. So when n = 2 the denominator is 2 + 4 = 6, and when n = 4 the denominator is 4 + 4= 8.
Hence, the rule can be,
f(n) = n/(n+4)
If n is even, then f(n) is positive.
If n is odd, then f(n) is negative.
Part C
56 is an even number.
As the function f(n) is positive when n is even, the sign of f(56) is positive.
Therefore, the answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.
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find the center and radius from the equation (x - 2)^2 + (y + 1)^2 = 16
Answer:
Center: (2,-1)
Radius: 4
Step-by-step explanation:
Circle equation: (x-h)^2 + (y-k)^2 = r^2
Finding the center:
Set to equaling 0 and solve for x and y
(x - 2)^2=0
(y + 1)^2=0
Finding the radius:
In the equation, because it's set to r^2, you would undo the square.
[tex]\sqrt{16}[/tex]=4
Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $900
Total amount = $1800
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/1200)^12t
T = A[tex](1+r/1200)^{12t}[/tex]
1800 = 900 (1+6/1200)^12t
2 = (1+1/200)^12t
2 = 1.005^12t
taking log on both sides
log 2 = 12t *log 1.005
0.3/0.002 = 12t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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Each marble bag sold by Ashley's Marble Company contains 3 green marbles for every 5 yellow marbles. If a bag has 18 green marbles, how many yellow marbles does it contain
Number of yellow marbles for every 18 green marbles = 30 yellow marbles
What is unitary method ?The unitary method entails figuring out the value of a single unit from which we can extrapolate the values of all the required units.
According to the given information
Applying the unitary method
Number of yellow marbles for every 3 green marbles = 5
Number of yellow marbles for every One green marbles = [tex]\frac{5}{3}[/tex]
Number of yellow marbles for every 18 green marbles = [tex]\frac{5}{3}[/tex] × 18
So
Number of yellow marbles for every 18 green marbles = 30 yellow marbles
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allison uses of a bag of horse feed per day. she feeds 2 quarter horses and 3 paint horses the same amount each day. draw a model to show a whole bag of horse feed below.
Allison feeds 11 horses in a day.
Horses are herbivores and, as such, they need a very specific diet. They must consume lots of fiber to keep their extremely long and sensitive digestive tract working and they must eat little and often, almost all day long.
A horse's feed should consist primarily of grass or roughage. However, hay is insufficient to provide a complete nutritional profile. Important minerals and nutrients will be added by adding grains and concentrates, but calories will also be added. Roughage, feeds, and concentration types are listed below, from least to most "complete."
Given,
Allison feeds 2 quarter horses and 3 paint horses the same amount each day.
Therefore, she feeds 2*4+3 = 11 horses in a day.
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Which expression is equivalent to (36−y2)
(
36
−
y
2
)
?
Responses
(36+12y+y2)
(
36
+
12
y
+
y
2
)
( 36 + 12 y + y 2 )
(36−12y+y2)
(
36
−
12
y
+
y
2
)
( 36 − − 12 y + y 2 )
(6−y)(6+y)
The equivalent expression to (36 - y²) is (6 - y) (6 + y).
The correct answer option is option C
Which is the equivalent expression?(36 - y²)
Check all options
A. (36 + 12y + y²)
No
B. (36 - 12y + y²)
No
C. (6 - y) (6 + y)
open parenthesis
= 36 + 6y - 6y - y²
= 36 - y²
Yes
D. (6 - y) (6 - y)
= 36 - 6y - 6y + y²
= 36 - 12y + y²
No
In conclusion, the expression (6 - y) (6 + y) is equivalent to (36 - y²)
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Kelly wants to fill 2 punch bowls for a birthday party. Each punch bowl holds 7 2/5 quarts of punch. How much punch will Kelly need?
Answer:
14 4/5
Step-by-step explanation: 7 2/5 x 2 or 7 2/5
+7 2/5
-------
14 4/5
Subtract 2w + 4 from 3w - 6
Answer:
w-10
Step-by-step explanation:
(3w-6)-(2w+4)
Take out the brackets:
3w-6-2w-4
Group the like terms:
3w-2w-6-4
Simplify:
w-10
the least common multiple of the two numbers is 40 the ratio of the greater number is the to the lessor number is 5, 4
if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.
What is Least Common Multiple (LCM)?Least Common Multiple is the meaning of the abbreviation LCM.
The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.
It can also be computed using two or more numbers.
Finding the LCM of a given collection of numbers can be done in a variety of ways.
Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.
The smallest number among all numbers is called the least common multiple of two or more numbers.
According to our question-
The number LCM is equal to 40.
4 × 5 × x = 40
20 × x = 40
20x=40
x=2
The larger number is equal to 4 x=4(2)=8.
The smaller value is =5x=5(2)=10.
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Complete question-
The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?
A 33-m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 34m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.
Answer:
8.2 m
Step-by-step explanation:
You want the length of the shadow whose tip is 34 m from the top of a 33 m building.
HypotenuseThe described geometry can be modeled by a right triangle with one leg 33 m and hypotenuse 34 m. The Pythagorean theorem tells us the length of the other leg is ...
a² +b² = c²
b² = c² -a²
b = √(c² -a²)
b = √(34² -33²) ≈ 8.2 . . . . meters
The length of the shadow is about 8.2 meters.
__
Additional comment
The angle of elevation to the top of the building can be found from the trig relation ...
Sin = Opposite/Hypotenuse
And the length of the shadow can be found from the relation ...
Cos = Adjacent/Hypotenuse
If α is the angle of elevation, then ...
sin(α) = 33/34 ⇒ α = arcsin(33/34)
and
Adjacent = Hypotenuse × cos(α)
Adjacent = 34·cos(arcsin(33/34)) ≈ 8.2 . . . . meters
where the "adjacent" side of the triangle is the side between the building and the tip of the shadow, along the ground.
Choose the letter of the correct equation for the graph
Using translation concepts, the equation for the graph is b.
y = cos(x + π/2) + 1
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Suppose that we've got:
f(x) = a cos (bx - c) + d
Then, this function has:
Amplitude (the maximum distance of the graph from the middle line) = a
Period =[tex]\dfrac{2\pi}{b}[/tex]
Phase shift = [tex]\dfrac{c}{b}[/tex]
Maximum value: a + d
Minimum value: -a + d
In this problem, we have a cosine function
(zero at π/2, this is zero at the origin), shifted π/2 units to the right and 1 unit up.
Since the standard amplitude is between -1 and 1, here is between 0 and 2).
Hence the rule is given as follows:
b. y = cos(x + π/2) + 1
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42 minus blank equals 29
Answer: 13
Step-by-step explanation:
Minus 29 from 42 to get 13
Answer:
13
Step-by-step explanation:
If you subtract 20 from 42, you will get your answer. Then you plug it into the equation to make sure it's correct.
42-29=13
29+13=42
42-13=29.
-Hope this helped
there are 12 levels in Zoe new video game suppose she plays the same number of levels each day what are all the possibilities for the number of days Zoe could play the game without repeating a level show you work ?
Answer:
17
Step-by-step explanation: